Holographic memory is the superdense packing of multidimensional information on a surface (the dimension of information is understood to be the number of independently varying parameters of the signal). The usual direct recording of a two-dimensional signal without noise on an \(L\times L\) area contains \(N^ 2\) bits, where \(N=L/L_ 0\) and \(L_ 0\) is the size of an elementary cell. Addition of each new unit of dimension leads to an increase of recording density by a factor N. Thus, even without special miniaturization (i.e., without decreasing \(L_ 0)\) a considerable density of memory can be achieved due to the size of the dimension of the signal being recorded.
Generally speaking, light waves are capable of carrying eight-dimensional information. Eight is the dimension of the set of bicharacteristics of Maxwell’s equations and the invariant vector-valued measures on them. However, the impossibility of fixing the amplitudes and phases of wave trains from real sources of light reduces this number to six. Holography makes it possible to record on a two-dimensional surface and reproduce all six of the remaining parameters of the signal. In the present note this assertion is spelled out and mathematically justified.